​ Solve: (x + 1) (x - 3) > 0, x R ​

Question

Solve:

(x + 1) (x - 3) > 0, x \(\in\) R

Answer 1

(x + 1)(x - 3) > 0

Therefore, \(x \in (-\infty,-1)\bigcup(3,\infty)\)

Answer 2

(x + 1) (x - 3) > 0, x \(\in\) R

⇒ x + 1 > 0 & x - 3 > 0 

or x + 1 < 0 & x - 3 < 0

(\(\because\) if ab > 0 then either a, b > 0 or a, b < 0)

⇒ x > - 1 & x > 3 or x < - 1 & x < 3

⇒ x > 3 or x < -1

⇒ x \(\in\) (3, \(\infty\)) or x \(\in\) (-\(\infty\), -1)

⇒ x \(\in\) (-\(\infty\), -1) U (3, \(\infty\))

Alternative:

(x + 1) (x - 3) > 0

\(\therefore\) x \(\in\) (-\(\infty\), -1) U (3, \(\infty\))